Response to sudden shifts in a two-nation arms race

Abstract

This article concerns living systems at the international or supranational level. Control theoretic techniques may be used to obtain information about the behavior of formal arms race models that cannot be gained by alternative methods. A two-nation, Richardson linear reaction process arms race model is treated as a second-order linear control system in order to determine its response to a sudden parameter shift represented as a step function disturbance. In contrast to the equilibrium oriented techniques generally used in the study of arms race models, control theoretic methods allow detailed analysis of both long-term and short-term effects of transient disturbances, including the way in which the system moves to a new equilibrium. The Routh-Hurwitz criteria and root-locus plot are compared to the more traditional stability criteria. System response is analyzed in detail for both the critically damped and the over- or under-damped cases. State space solution concepts that allow treatment of many-nation systems are examined. The techniques here applied to the arms expenditures of two nations isolated from or only loosely coupled to the rest of the world are also applicable to other reaction processes, such as two-party or intergroup conflicts, and this treatment may be extended both to higher-order differential equation models and to a large class of nonlinear models. Some methods are suggested for governments to use in managing their behavior so as to bring sudden shifts in arms races under greater control.